Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C42×((C3⋊D3)⋊C3)⋊C2 |
| Fitting | C42×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | H(3,𝔽3) ⋊ C22×C42 |
1851 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 1851 conjugacy classes of subgroups — too many to draw. Only its 387 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C42×AGL(2,𝔽3), #127×((C3⋊D3)⋊C3)⋊C2, #97×((C3⋊D3)⋊C3)⋊C2 |
| maximal normal subgroup of | #127×((C3⋊D3)⋊C3)⋊C2, #97×((C3⋊D3)⋊C3)⋊C2 |
| maximal quotient of | #97×((C3⋊D3)⋊C3)⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13955);